Problem: $h(n) = 7n+1+4(g(n))$ $g(t) = -t$ $f(x) = -2x+g(x)$ $ f(h(-5)) = {?} $
First, let's solve for the value of the inner function, $h(-5)$ . Then we'll know what to plug into the outer function. $h(-5) = (7)(-5)+1+4(g(-5))$ To solve for the value of $h$ , we need to solve for the value of $g(-5)$ $g(-5) = -(-5)$ $g(-5) = 5$ That means $h(-5) = (7)(-5)+1+(4)(5)$ $h(-5) = -14$ Now we know that $h(-5) = -14$ . Let's solve for $f(h(-5))$ , which is $f(-14)$ $f(-14) = (-2)(-14)+g(-14)$ To solve for the value of $f$ , we need to solve for the value of $g(-14)$ $g(-14) = -(-14)$ $g(-14) = 14$ That means $f(-14) = (-2)(-14)+14$ $f(-14) = 42$